153 1.5 Applications and Modeling with Quadratic Equations Relating Concepts For individual or collaborative investigation (Exercises 57–60) If p units of an item are sold for x dollars per unit, the revenue is R = px. Use this idea to analyze the following problem, working Exercises 57–60 in order. Number of Apartments Rented The manager of an 80-unit apartment complex knows from experience that at a rent of $300, all the units will be full. On the average, one additional unit will remain vacant for each $20 increase in rent over $300. Furthermore, the manager must keep at least 30 units rented due to other financial considerations. Currently, the revenue from the complex is $35,000. How many apartments are rented? 57. Suppose that x represents the number of $20 increases over $300. Represent the number of apartment units that will be rented in terms of x. 58. Represent the rent per unit in terms of x. 59. Use the answers in Exercises 57 and 58 to write an equation that defines the revenue generated when there are x increases of $20 over $300. 60. According to the problem, the revenue currently generated is $35,000. Substitute this value for revenue into the equation from Exercise 59. Solve for x to answer the question in the problem. Solve each problem. (See Exercises 57–60.) 61. Number of Airline Passengers The cost of a charter flight to Miami is $225 each for 75 passengers, with a refund of $5 per passenger for each passenger in excess of 75. How many passengers must take the flight to produce a revenue of $16,000? 62. Number of Bus Passengers A charter bus company charges a fare of $40 per person, plus $2 per person for each unsold seat on the bus. If the bus holds 100 passengers and x represents the number of unsold seats, how many passengers must ride the bus to produce revenue of $5950? (Note: Because of the company’s commitment to efficient fuel use, the charter bus will not run unless filled to at least half-capacity.) 63. Harvesting a Cherry Orchard The manager of a cherry orchard wants to schedule the annual harvest. If the cherries are picked now, the average yield per tree will be 100 lb, and the cherries can be sold for 40 cents per pound. Past experience shows that the yield per tree will increase about 5 lb per week, while the price will decrease about 2 cents per pound per week. How many weeks should the manager wait to get an average revenue of $38.40 per tree? 64. Recycling Aluminum Cans A local group of scouts has been collecting old aluminum cans for recycling. The group has already collected 12,000 lb of cans, for which they could currently receive $4 per hundred pounds. The group can continue to collect cans at the rate of 400 lb per day. However, a glut in the old-can market has caused the recycling company to announce that it will lower its price, starting immediately, by $0.10 per hundred pounds per day. The scouts can make only one trip to the recycling center. How many days should they wait in order to receive $490 for their cans?
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